$Ab$ $initio$ low-energy effective Hamiltonians for high-temperature superconducting cuprates Bi$_2$Sr$_2$CuO$_6$, Bi$_2$Sr$_2$CaCu$_2$O$_8$, HgBa$_2$CuO$_4$ and CaCuO$_2$

Jean-Baptiste Morée; Motoaki Hirayama; Michael Thobias Schmid; Youhei Yamaji; Masatoshi Imada

doi:10.1103/PhysRevB.106.235150

paper

$A b$ $ini t i o$ low-energy effective Hamiltonians for high-temperature superconducting cuprates Bi $_{2}$ Sr $_{2}$ CuO $_{6}$ , Bi $_{2}$ Sr $_{2}$ CaCu $_{2}$ O $_{8}$ , HgBa $_{2}$ CuO $_{4}$ and CaCuO $_{2}$

arXiv:2206.01510 · doi:10.1103/PhysRevB.106.235150

Abstract

We derive $ab$ $ini t i o$ low-energy effective Hamiltonians (LEH) for high-temperature superconducting (SC) copper oxides Bi $_{2}$ Sr $_{2}$ CuO $_{6}$ (Bi2201, $N_{ℓ} = 1$ , $T_{c}^{exp} \sim 10$ K), Bi $_{2}$ Sr $_{2}$ CaCu $_{2}$ O $_{8}$ (Bi2212, $N_{ℓ} = 2$ , $T_{c}^{exp} \sim 84$ K), HgBa $_{2}$ CuO $_{4}$ (Hg1201, $N_{ℓ} = 1$ , $T_{c}^{exp} \sim 90$ K) and CaCuO $_{2}$ (Ca11, $N_{ℓ} = \infty$ , $T_{c}^{exp} \sim 110$ K), with different experimental optimal SC transition temperature $T_{c}^{exp}$ and number $N_{ℓ}$ of laminated CuO $_{2}$ planes between the two neighboring block layers. We apply the latest methodology of the multiscale $ab$ $ini t i o$ scheme for correlated electron systems (MACE), and focus on the LEH consisting of one antibonding (AB) Cu $3 d_{x^{2} - y^{2}}$ /O $2 p_{σ}$ orbital centered on each Cu atom. We discuss prominent features of this LEH: (1) The ratio $U /∣ t_{1} ∣$ between the onsite effective Coulomb repulsion (ECR) $U$ and amplitude of nearest neighbour hopping $t_{1}$ increases with $T_{c}^{exp}$ and $N_{ℓ}$ , consistently with the expected increase in $d$ -wave SC correlation function $P_{dd}$ with $U /∣ t_{1} ∣$ . One possible cause of the increase of $U /∣ t_{1} ∣$ is the replacement of apical O atoms by Cu atoms from neighbouring CuO $_{2}$ planes when $N_{ℓ}$ increases. Furthermore, we show that the increase in distance between Cu and apical O atoms decreases the effective screening (ES) by electrons outside of the LEH and increases $U /∣ t_{1} ∣$ . (2) For Hg1201 and Ca11, we show that $U /∣ t_{1} ∣$ decreases when hole doping per AB orbital $δ$ increases, which may partly account for the disappearance of SC when $δ$ exceeds the optimal value in experiment. (3) For $N_{ℓ} \geq 2$ , off-site inter-CuO $_{2}$ plane ECR is comparable to off-site intra-CuO $_{2}$ plane ECR. We discuss contributions of inter-CuO $_{2}$ plane ECR to both $P_{dd}$ and the stability of the SC state.

arXiv comment26 pages, 8 figures, 11 tables. The Supplemental Material contains the complete list of parameters for effective Hamiltonians presented in the main text, as well as complementary effective Hamiltonians mentioned in Footnote 1 (Page 2) and Footnote 2 (Page 3). This Supplemental Material may be obtained from the authors upon request

$A b$ $ini t i o$ low-energy effective Hamiltonians for high-temperature superconducting cuprates Bi $_{2}$ Sr $_{2}$ CuO $_{6}$ , Bi $_{2}$ Sr $_{2}$ CaCu $_{2}$ O $_{8}$ , HgBa $_{2}$ CuO $_{4}$ and CaCuO $_{2}$

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Ab initio low-energy effective Hamiltonians for high-temperature superconducting cuprates Bi2​Sr2​CuO6​, Bi2​Sr2​CaCu2​O8​, HgBa2​CuO4​ and CaCuO2​

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Cited by in corpus (20)

$A b$ $ini t i o$ low-energy effective Hamiltonians for high-temperature superconducting cuprates Bi $_{2}$ Sr $_{2}$ CuO $_{6}$ , Bi $_{2}$ Sr $_{2}$ CaCu $_{2}$ O $_{8}$ , HgBa $_{2}$ CuO $_{4}$ and CaCuO $_{2}$